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Common Core Math5th GradeFractions

5.NF.2: Solve Fraction Word Problems

Also written as 5.NF.A.2 and CCSS.MATH.CONTENT.5.NF.A.2 · Cluster: Use equivalent fractions as a strategy to add and subtract fractions.

Make 5.NF.2 Word ProblemsAll 26 5th Grade Math Standards

The Official Wording

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Common Core State Standards, Grade 5, Number & Operations: Fractions · Read it at the source · Checked October 14, 2026

What 5.NF.2 Means in Plain English

Fifth graders solve stories like this one: Maya ran 3/4 mile before school and 2/5 mile after. How far did she run? They draw a model or write 3/4 + 2/5 = 15/20 + 8/20 = 23/20, then report 1 3/20 miles.

The second half of the standard is the estimate. Before computing, students reason that 3/4 is near 1 and 2/5 is under 1/2, so the answer should land a little over 1 mile. That habit carries into fraction multiplication problems (5.NF.6) and 7th-grade rational-number problems (7.NS.3).

5.NF.2 I Can Statements

  • I can solve a word problem that adds or subtracts fractions.
  • I can estimate with benchmarks like 1/2 and 1 before I compute.
  • I can explain why an answer like 3/7 cannot be right.

5.NF.2 Worked Example

A baking problem where the estimate comes first and says “close to 1, maybe over,” so the exact sum has to settle it.

Problem

A recipe calls for 2/3 cup of white flour and 3/8 cup of whole wheat flour. Together, does the flour fit in a 1-cup measuring cup?

Does the flour fit in a 1-cup measure?
  1. Estimate first. 2/3 is more than 1/2, and 3/8 is a little less than 1/2. The total is close to 1 cup, maybe just over, so we need the exact sum to decide.2/3 > 1/2, 3/8 < 1/2, total near 1
  2. Thirds and eighths need a common denominator. 24 is the smallest number both 3 and 8 divide into.2/3 = 16/24, 3/8 = 9/24
  3. Add the twenty-fourths.16/24 + 9/24 = 25/24
  4. 25/24 is one whole and 1/24 more, so the flour is just over 1 cup.25/24 = 1 1/24 cups
Answer1 1/24 cups, so it does not quite fit in a 1-cup measure

Check it: The estimate said close to 1 and maybe over, and 1 1/24 is just over. A result like 5/11 (adding tops and bottoms) would fail the estimate at once, since 5/11 is less than 1/2.

Common Mistakes with 5.NF.2

Adding tops and bottoms

2/5 + 1/2 = 3/7

Try this: Check against a benchmark: 1/2 alone is bigger than 3/7, so adding more cannot give 3/7. Then find tenths: 4/10 + 5/10.

Choosing the wrong operation

“How much more” read as adding: 3/4 + 1/3 instead of 3/4 − 1/3

Try this: Draw both amounts as bars on the same whole before writing anything. Comparing two bars shows the gap, which is a subtraction.

Skipping the reasonableness check

7/8 − 1/4 = 6/4, written down and moved on

Try this: Ask whether taking away can leave more than you started with. 7/8 is under 1, so 6/4 (over 1) must be wrong.

Where 5.NF.2 Fits

Comes Before4.NF.3Add and subtract fractions with like denominators in word problems.4.NF.2Compare fractions using benchmarks like 1/2.
Alongside5.NF.1The computation itself: rewriting with a common denominator.5.MD.2Use fraction operations on measurements shown in a line plot.
Comes Next5.NF.6Word problems that multiply fractions and mixed numbers.7.NS.3Solve problems with all four operations on rational numbers, negatives included.

Practice 5.NF.2

Word Problem GeneratorFree ToolAddition and subtraction stories whose fractions share one whole, so students practice the estimate and then the exact answer.AdditionSubtractionFractions
Make Word Problems

Quick Check

  1. Without computing, is 3/5 + 1/2 more or less than 1? How do you know?
  2. Leo drank 3/4 liter of water in the morning and 5/8 liter in the afternoon. How much did he drink in all?
  3. A board is 5/6 meter long. Ana cuts off 1/4 meter. How much is left?

5.NF.2: Other Names

5.NF.25.NF.A.2CCSS.MATH.CONTENT.5.NF.A.2

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.